Home
Class 12
MATHS
Prove that cosecA-2 cot 2A cos A=2sinA....

Prove that `cosecA-2 cot 2A cos A=2sinA.`

Text Solution

Verified by Experts

`co sec A-2 cot 2A cos A=(1)/(sin A)-(2cos 2A cosA)/(sin 2A)`
`=(1)/(sin A)-(2cos 2A cos A)/(2ssin A cos A)`
`(1)/(sin A)-(cos 2A)/(sinA)`
`=(1-cos 2A)/(sinA)`
`=(2sin^(2)A)/(sin A)`
`=2sinA`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.5|6 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.6|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.3|13 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that cos2A=cos^2 A -sin^2 A

Prove that cos A cos 2A cos 2^(2) A cos 2^(3)A....cos 2^(n-1) A=(sin 2^(n) A)/(2^(n) sin A)

If cos(A+B)sin(C+D)=cos(A-B)sin(C-D) , prove that cot A cot B cot C=cotD .

Prove that ((cos^3A-sin^3A)/(cosA - sinA))- ((cos^3A + sin^3A)/(cosA + sinA))= 2sin A cos A

Prove that (1+sin2A)/(cos2A)=(cosA+sinA)/(cosA-sinA)=tan((pi)/(4)+A)

Prove that (cos 3x +cos 7x - cos 2x )/( sin 7x - sin 3x - sin 2x ) = cot 2x

Prove that cos (A + B) cos (A - B) = cos^(2) B - sin^(2) A

Prove that cos (A + B) cos (A - B) = cos^(2) A - sin^(2) B = cos^(2) B- sin^(2) A

If A + B + C = (pi)/(2) , prove that cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B cos C

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2...

    Text Solution

    |

  2. Prove that tan ((pi)/(4) + theta)- tan ((pi)/(4) - theta) = 2 tan 2 th...

    Text Solution

    |

  3. Prove that cosecA-2 cot 2A cos A=2sinA.

    Text Solution

    |

  4. Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 ...

    Text Solution

    |

  5. (sin ^2 3A )/( sin ^2 A ) -( cos^2 3A )/(cos ^2 A ) is

    Text Solution

    |

  6. Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/...

    Text Solution

    |

  7. If in an isosceles triangle with base 'a', vertical angle 20^@ and lat...

    Text Solution

    |

  8. In DeltaABC, a = 3, b = 4 and c = 5, then value of sinA + sin2B + sin...

    Text Solution

    |

  9. If cos A = 3/4 then sin ""(A) /(2 ) . Sin 5 (A)/(2) is

    Text Solution

    |

  10. Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@...

    Text Solution

    |

  11. If theta is an acute angle and sin((theta)/(2))=sqrt((x-1)/(2x)) ,then...

    Text Solution

    |

  12. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

    Text Solution

    |

  13. Let a=(pi)/(7), then (a) show that sin^(2)3a-sin^(2)a=sin2asin3a (...

    Text Solution

    |

  14. Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

    Text Solution

    |

  15. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

    Text Solution

    |

  16. If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value...

    Text Solution

    |

  17. tantheta+tan(6 0^0+theta)+tan(12 0^0+theta)=3tan3theta

    Text Solution

    |

  18. If A=110^(@), then prove that (1+sqrt(1+tan^(2)2A))/(tan2A)=-tan A.

    Text Solution

    |

  19. If alpha and beta are the two different roots of equations alpha cos t...

    Text Solution

    |

  20. If tan beta=cos theta tan alpha, then prove that tan^(2)""(theta)/(2)=...

    Text Solution

    |